Archive for covariance

What are the distributions on the positive k-dimensional quadrant with parametrizable covariance matrix?

Posted in Books, pictures, Statistics, University life with tags , , , , , , on March 30, 2012 by xi'an

This is the question I posted this morning on StackOverflow, following an exchange two days ago with a user who could not see why the linear transform of a log-normal vector X,

Y = μ + Σ X

could lead to negative components in Y…. After searching a little while, I could not think of a joint distribution on the positive k-dimensional quadrant where I could specify the covariance matrix in advance. Except for a pedestrian construction of (x1,x2) where x1 would be an arbitrary Gamma variate [with a given variance] and x2 conditional on x1 would be a Gamma variate with parameters specified by the covariance matrix. Which does not extend nicely to larger dimensions.